I guess it comes down to whether a bodge could pass muster. Yes, tapers do the work - but the darn nut has to stay on . . . I'd be uneasy just running another die up the thing, have to say, unless - maybe - I could cross-drill the shaft and use a castellated nut and a small split pin to be certain it couldn't fall off. Or something.
I'm the first to do things that aren't 'correct spec' when faced with these sorts of things, but I'm a bit picky about the execution of workarounds.
A bodged fastener whirring round in there would worry me (needlessly possibly, but it would), so I would either do what Trevinoz suggests, which would be a workmanlike solution, or I'd turn off the rest of the dud thread and put on a new one (of whatever series required the least reduction in diameter to get to the exact size for the die).
I would then make a new nut from a bit of hex the same AF or near as dammit as the original, tapping it to be a good 90% fit (ie a bit more than typical), and thereby ensure that the thing sat just like the original.
To do either properly it does needs a lathe, I know. But . . .
Or I'd get another shaft if they can be had.